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We have investigated the role of localized {it d} bands in the dynamical response of Au, on the basis of {it ab initio} pseudopotential calculations. The density-response function has been evaluated in the random-phase approximation. For small momenta, we have found a double peak structure in the energy-loss function, which results from the presence of {it d} electrons. These results are in good agreement with the experimentally determined optical response of gold. We also analyze the dependence of the dynamical structure factor on the wave vector {bf q}.
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The electron energy-loss function of graphite is studied for momentum transfers q beyond the first Brillouin zone. We find that near Bragg reflections the spectra can change drastically for very small variations in q. The effect is investigated by means of first principle calculations in the random phase approximation and confirmed by inelastic x-ray scattering measurements of the dynamic structure factor S(q,omega). We demonstrate that this effect is governed by crystal local field effects and the stacking of graphite. It is traced back to a strong coupling between excitations at small and large momentum transfers.
We combine the results of perturbative continuous unitary transformations with a mean-field calculation to determine the evolution of the single-mode, i.e., one-triplon, contribution to the dynamic structure factor of a two-leg $S=1/2$ ladder on increasing temperature from zero to a finite value. The temperature dependence is induced by two effects: (i) no triplon can be excited on a rung where a thermally activated triplon is present; (ii) conditional excitation processes take place if a thermally activated triplon is present. Both effects diminish the one-triplon spectral weight upon heating. It is shown that the second effect is the dominant vertex correction in the calculation of the dynamic structure factor. The matrix elements describing the conditional triplon excitation in the two-leg Heisenberg ladder with additional four-spin ring exchange are calculated perturbatively up to order 9. The calculated results are compared to those of an inelastic neutron scattering experiment on the cuprate-ladder compound La$_{4}$Sr$_{10}$Cu$_{24}$O$_{41}$ showing convincing agreement for established values of the exchange constants.
An analytical approach is developed to the problem of computation of monotone Riemannian metrics (e.g. Bogoliubov-Kubo-Mori, Bures, Chernoff, etc.) on the set of quantum states. The obtained expressions originate from the Morozova, Chencov and Petz correspondence of monotone metrics to operator monotone functions. The used mathematical technique provides analytical expansions in terms of the thermodynamic mean values of iterated (nested) commutators of a model Hamiltonian T with the operator S involved through the control parameter $h$. Due to the sum rules for the frequency moments of the dynamic structure factor new presentations for the monotone Riemannian metrics are obtained. Particularly, relations between any monotone Riemannian metric and the usual thermodynamic susceptibility or the variance of the operator $S$ are discussed. If the symmetry properties of the Hamiltonian are given in terms of generators of some Lie algebra, the obtained expansions may be evaluated in a closed form. These issues are tested on a class of model systems studied in condensed matter physics.
We study the effect of a one dimensional periodic potential on the dynamic structure factor of an interacting Bose Einstein condensate at zero temperature. We show that, due to phononic correlations, the excitation strength towards the first band develops a typical oscillating behaviour as a function of the momentum transfer, and vanishes at even multiples of the Bragg momentum. The effects of interactions on the static structure factor are found to be significantly amplified by the presence of the optical potential. Our predictions can be tested in stimulated photon scattering experiments.
The dynamic spin structure factor $mathcal{S}(k,omega)$ of a system of spin-1/2 bosons is investigated at arbitrary strength of interparticle repulsion. As a function of $omega$ it is shown to exhibit a power-law singularity at the threshold frequency defined by the energy of a magnon at given $k.$ The power-law exponent is found exactly using a combination of the Bethe Ansatz solution and an effective field theory approach.
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